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Acceleration Due To Gravity

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Question

Three blocks of mass $m_{1} = 4 k g, m_{2} = 2 k g, m_{3} = 4 k g$ are connected as shown in figure. All surfaces are smooth and pulley is massless, find the acceleration of mass $m_{1}$ ?

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Solution

As all pulleys are massless so treating second pulley connecting mass $m_{2}$ $a n d$ $m_{3}$ as a combined mass i.e., $m_{2} + m_{3}$ .

$m_{1}$ has only one horizontal force i.e. tension $T$ ,if it has acceleration $a$ then we have from Newton's second Law

$T = m_{1} a = 4 a$ as $m_{1} = 4 K g$ ...........1

As the combined mass and mass $m_{1}$ are connected by same string so it should have same acceleration $a$ , $SEE the figure$ .

now Equation for combined mass is net downward Force = mass multiplied by acceleration
or $(m_{2} + m_{3}) g - T = (m_{2} + m_{3}) a$ put values of masses and $T = 4 a$ we get $a = 0.6 m s^{- 2}$

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